Adjoint Greeks Made Easy
Luca Capriotti and Michael Giles
Adjoint Greeks Made Easy
Introduction
Preface to Chapter 1
Being Two-Faced over Counterparty Credit Risk
Risky Funding: A Unified Framework for Counterparty and Liquidity Charges
DVA for Assets
Pricing CDSs’ Capital Relief
The FVA Debate
The FVA Debate: Reloaded
Regulatory Costs Break Risk Neutrality
Risk Neutrality Stays
Regulatory Costs Remain
Funding beyond Discounting: Collateral Agreements and Derivatives Pricing
Cooking with Collateral
Options for Collateral Options
Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs
In the Balance
Funding Strategies, Funding Costs
The Funding Invariance Principle
Regulatory-Optimal Funding
Close-Out Convention Tensions
Funding, Collateral and Hedging: Arbitrage-Free Pricing with Credit, Collateral and Funding Costs
Bilateral Counterparty Risk with Application to Credit Default Swaps
KVA: Capital Valuation Adjustment by Replication
From FVA to KVA: Including Cost of Capital in Derivatives Pricing
Warehousing Credit Risk: Pricing, Capital and Tax
MVA by Replication and Regression
Smoking Adjoints: Fast Evaluation of Monte Carlo Greeks
Adjoint Greeks Made Easy
Bounding Wrong-Way Risk in Measuring Counterparty Risk
Wrong-Way Risk the Right Way: Accounting for Joint Defaults in CVA
Backward Induction for Future Values
A Non-Linear PDE for XVA by Forward Monte Carlo
Efficient XVA Management: Pricing, Hedging and Allocation
Accounting for KVA under IFRS 13
FVA Accounting, Risk Management and Collateral Trading
Derivatives Funding, Netting and Accounting
Managing XVA in the Ring-Fenced Bank
XVA: A Banking Supervisory Perspective
An Annotated Bibliography of XVA
The renewed emphasis of the financial industry on quantitatively sound risk management practices comes with formidable computational challenges. Computationally intensive Monte Carlo simulations are often the only practical tool available, and standard approaches for the calculation of risk require repeated simulation of a portfolio’s profit and loss.
Several faster alternative methods for the calculation of price sensitivities have been proposed in the literature (for a review see, for example, Glasserman 2004). Among these, the pathwise derivative method (Broadie and Glasserman 1996) provides unbiased estimates at a computational cost that may be smaller than standard finite-differences approaches. A very efficient implementation of the pathwise derivative method was proposed in Giles and Glasserman (2006) in the context of the London Interbank Offered Rate (Libor) market model (LMM) for European payouts. This was later generalised to Bermudan options by Leclerc et al (2009) and extended by Denson and Joshi (2011). The latter express the calculation of the pathwise derivative estimator in terms of linear algebra operations, and use adjoint methods to reduce the overall
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